Space of modular forms of level 1305, weight 2, and Character 1305.cf

• Label: 1305.2.cf
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.cf
• Rep. character: $\chi_{1305}(44,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $720$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.cf (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 435 \)
Character field:			\(\Q(\zeta_{28})\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1305, [\chi])\).

	Total	New	Old
Modular forms	2256	720	1536
Cusp forms	2064	720	1344
Eisenstein series	192	0	192

Trace form

\( 720 q - 4 q^{10} + 120 q^{16} - 16 q^{19} + 20 q^{40} - 16 q^{46} + 216 q^{49} + 80 q^{55} - 56 q^{61} + 280 q^{70} - 432 q^{76} + 136 q^{85} - 336 q^{91} + 64 q^{94}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1305, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1305, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)